Insert Keyframe reverses Mirror option?
Insert Keyframe will only create keyframes for the selected bone(s), not for all the bones of your armature. You've only selected one bone in your video, the mirrored bone will also move because of the X mirror option, but it won't be taken into account as it is not selected.
All Channels means that it will create keyframes for all the channels of this bone (Location, Rotation and Scale).
If you want the rotation to be taken account for all your bones, activate the Auto Keying option, but in that case you don't need to insert a keyframe.
Also, try to not report a bug if you're not sure it's a bug.